FM Harmonic Amplitudes (Bessel Functions)

FM bandwidth expands as the modulation-amplitude $A_m$ is increased in (G.2) above. The $k$ th harmonic amplitude is proportional to the $k$ th-order Bessel function of the first kind $J_k$ , evaluated at the FM modulation index $\beta=A_m$ . Figure G.7 illustrates the behavior of $J_k(\beta)$ : As $\beta$ is increased, more power appears in the sidebands, at the expense of the fundamental. Thus, increasing the FM index brightens the tone.

Figure: Bessel functions of the first kind for a range of orders (harmonic numbers) $k$ and argument (FM index) $\beta$ (from [264]).